Student Research Projects&lt;BR&gt; Goursat's Other Theorem

Petrillo, Joseph

doi:10.4169/193113409x469569

Cited by 8 publications

(2 citation statements)

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“…A recent paper in this JOURNAL [5] outlines a proof of Goursat's theorem which shows how to construct a subgroup U of G 1 × G 2 given two isomorphic quotients, and vice-versa. Figure 1 then determine all isomorphisms between pairs of isomorphic quotients, then one can count the subgroups of G 1 × G 2 by counting all such triples.…”

Section: Goursat's Theoremmentioning

confidence: 99%

Counting Subgroups in a Direct Product of Finite Cyclic Groups

Petrillo

2011

The College Mathematics Journal

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to The College Mathematics Journal. ) earned his Ph.D.from Binghamton University in 2003. He is currently an associate professor of mathematics and holds the endowed Cole Chair in Mathematics at Alfred University in beautiful western New York. His main research focuses on subgroup properties in finite groups. He enjoys teaching, problem solving, playing guitar, and enjoying life with his wife, Lynn, and his son, Julian.

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Section: Goursat's Theoremmentioning

confidence: 99%

Counting Subgroups in a Direct Product of Finite Cyclic Groups

Petrillo

2011

The College Mathematics Journal

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“…Other researchers have extensively used Goursat's Theorem to advance algebra [3][4][5][8][9][10][11][12][13][14][15]. Therefore, this theorem is important to be studied in more depth; for example, Bauer et al [12] generalize to a direct product of groups by designing an asymmetric ICMScE version of Goursat's Theorem for the two groups and then applying recursively.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Goursat's Theorem for Subrings of Direct Products of n Rings

Lieko Liedokto,

Susanto,

Sulandra

2024

KLS

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Bauer et al. describe Goursat’s theorem, representing the characteristics of subgroups of a direct product of two or more groups. In this paper, we expand into a ring structure that describes the characteristics of subrings of a direct product of rings. This research method is to analogize the evidence by Bauer et al. in the group for generalization. In our main results, every subring of the direct product of rings is determined by ring epimorphism between the ring and factor ring. Keywords: Goursat’s theorem, subrings, rings

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